Geodesic
Intersection theory and Hilbert function
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 82-94

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Birationally invariant intersection theory is a far-reaching generalization and extension of the Bernstein–Kushnirenko theorem. This paper presents transparent proofs of Hilbert's theorem on the degree of a projective variety and other related statements playing an important role in this theory. The paper is completely self-contained; we recall all necessary definitions and statements.
Keywords: degree of projective variety, Hilbert function, intersection theory, Bernstein–Kushnirenko theorem. 
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     author = {A. G. Khovanskii},
     title = {Intersection theory and {Hilbert} function},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a7/}
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A. G. Khovanskii. Intersection theory and Hilbert function. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 82-94. http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a7/